Problem: Simplify the following expression: $\dfrac{18r^4}{15r}$ You can assume $r \neq 0$.
Explanation: $ \dfrac{18r^4}{15r} = \dfrac{18}{15} \cdot \dfrac{r^4}{r} $ To simplify $\frac{18}{15}$ , find the greatest common factor (GCD) of $18$ and $15$ $18 = 2 \cdot 3 \cdot 3$ $15 = 3 \cdot 5$ $ \mbox{GCD}(18, 15) = 3 $ $ \dfrac{18}{15} \cdot \dfrac{r^4}{r} = \dfrac{3 \cdot 6}{3 \cdot 5} \cdot \dfrac{r^4}{r} $ $\phantom{ \dfrac{18}{15} \cdot \dfrac{4}{1}} = \dfrac{6}{5} \cdot \dfrac{r^4}{r} $ $ \dfrac{r^4}{r} = \dfrac{r \cdot r \cdot r \cdot r}{r} = r^3 $ $ \dfrac{6}{5} \cdot r^3 = \dfrac{6r^3}{5} $